Related papers: Latent Mode Decomposition
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Accurate extraction of multicomponent linear frequency modulation (LFM) signal parameters, such as onset frequency, linear modulation frequency, amplitude, and initial phase, is of great importance in the fields of ISAR, cognitive radio,…
Time series decomposition into trend, seasonal structure, and residual components is a core primitive for downstream analytics such as anomaly detection, change-point detection, and forecasting. However, most existing seasonal-trend…
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
Understanding the internal functional organization of Large Language Models (LLMs) is crucial for improving their trustworthiness and performance. However, how LLMs organize different functions into modules remains highly unexplored. To…
Recent advances in Multimodal Large Language Models (MLLMs) have shown impressive reasoning capabilities across vision-language tasks, yet still face the challenge of compute-difficulty mismatch. Through empirical analyses, we identify that…
Singular value decomposition (SVD) is widely used in wireless systems, including multiple-input multiple-output (MIMO) processing and dimension reduction in distributed MIMO (D-MIMO). However, the iterative nature of decomposition methods…
This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for…
Accurate spatiotemporal forecasting is critical for numerous complex systems but remains challenging due to complex volatility patterns and spectral entanglement in conventional graph neural networks (GNNs). While decomposition-integrated…
Latent Variable Models (LVMs) are a large family of machine learning models providing a principled and effective way to extract underlying patterns, structure and knowledge from observed data. Due to the dramatic growth of volume and…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…
We present the Latent Sequence Decompositions (LSD) framework. LSD decomposes sequences with variable lengthed output units as a function of both the input sequence and the output sequence. We present a training algorithm which samples…
Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…
The prevalent fully-connected tensor network (FCTN) has achieved excellent success to compress data. However, the FCTN decomposition suffers from slow computational speed when facing higher-order and large-scale data. Naturally, there…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
We present a deep-learning Variational Encoder-Decoder (VED) framework for learning data-driven low-dimensional representations of the relationship between high-dimensional parameters of a physical system and the system's high-dimensional…